We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Recent advances in sensor and mobile devices have enabled an unprecedented increase in the availability and collection of urban trajectory data, thus increasing the demand for more efficient ways to manage and analyze the data being produced. In this survey, we comprehensively review recent research trends in trajectory data management, ranging from trajectory pre-processing, storage, common trajectory analytic tools, such as querying spatial-only and spatial-textual trajectory data, and trajectory clustering. We also explore four closely related analytical tasks commonly used with trajectory data in interactive or real-time processing. Deep trajectory learning is also reviewed for the first time. Finally, we outline the essential qualities that a trajectory data management system should possess in order to maximize flexibility.

A Survey on Trajectory Data Management, Analytics, and Learning

Recent advances in sensor and mobile devices have enabled an unprecedented increase in the availability and collection of urban trajectory data, thus increasing the demand for more efficient ways to manage and analyze the data being produced. In this survey, we comprehensively review recent research trends in trajectory data management, ranging from trajectory pre-processing, storage, common trajectory analytic tools, such as querying spatial-only and spatial-textual trajectory data, and trajectory clustering. We also explore four closely related analytical tasks commonly used with trajectory data in interactive or real-time processing. Deep trajectory learning is also reviewed for the first time. Finally, we outline the essential qualities that a trajectory data management system should possess to maximize flexibility.

Point-of-interest (POI) recommendations can help users effectively explore new locations according to their preferences, which is an important research aspect for location-based social networks (LBSNs) However, most existing POI recommendation methods lack adaptability when making recommendations for users with different preferences, which causes unsatisfactory recommendation results To this end, in this paper, we propose an adaptive POI recommendation method by combining user activity and spatial features, which can operate adaptively according to user activity First, we extract three-dimensional user activity, time-based POI popularity and distance features using a probabilistic statistical analysis method from historical check-in datasets on LBSNs Second, we devise a user activity clustering algorithm that is based on fuzzy c-means and compute POI popularity by applying smoothing technology to adjacent continuous time slots Finally, we propose an adaptive recommendation scheme, which includes a two-dimensional Gaussian kernel density estimation algorithm and a one-dimensional power-law function algorithm with POI popularity according to user activity Extensive experiments on Foursquare and Gowalla datasets show that the proposed method outperforms the baseline methods in terms of both precision and recall

An adaptive point-of-interest recommendation method for location-based social networks based on user activity and spatial features

For real-world time dependent road networks (TDRNs), answering shortest path-based route queries and plans in real-time is highly desirable by many industrial applications. Unfortunately, traditional (Dijkstra- or A*-like) algorithms are computationally expensive for such tasks on TDRNs.Naturally, indexes are needed to meet the real-time constraint required by real applications. In this paper, we propose a novel height-balanced tree-structured index, called TD-G-tree, which supports fast route queries over TDRNs. The key idea is to use hierarchical graph partitioning to split a road network into hierarchical partitions. This will produce a balanced tree, where each tree node corresponds to a partition and each parent-child relationship corresponds to a partition and its sub-partition. We then compute and index time dependent shortest paths (TDSPs) only for borders (i.e., vertices whose edges are cut by a partition). Based on TD-G-tree, we devise efficient algorithms to support TDSP queries, as well as time-interval based route planning, for computing optimal solutions through dynamic programming and chronological divide-and-conquer. Extensive experiments on real-world datasets show that our method significantly outperforms existing approaches.

/pdf/querying-shortest-paths-on-time-dependent-road-networks-2y6j93unjj.pdf

Querying shortest paths on time dependent road networks

For thousands of years, people have been innovating new technologies to make their travel faster, the latest of which is GPS technology that is used by millions of drivers every day. The routes recommended by a GPS device are computed by path planning algorithms (e.g., fastest path algorithm), which aim to minimize a certain objective function (e.g., travel time) under the current traffic condition. When the objective is to arrive the destination as early as possible, waiting during travel is not an option as it will only increase the total travel time due to the First-In-First-Out property of most road networks. However, some businesses such as logistics companies are more interested in optimizing the actual on-road time of their vehicles (i.e., while the engine is running) since it is directly related to the operational cost. At the same time, the drivers' trajectories, which can reveal the traffic conditions on the roads, are also collected by various service providers. Compared to the existing speed profile generation methods, which mainly rely on traffic monitor systems, the trajectory-based method can cover a much larger space and is much cheaper and flexible to obtain. This paper proposes a system, which has an online component and an offline component, to solve the minimal on-road time problem using the trajectories. The online query answering component studies how parking facilities along the route can be leveraged to avoid predicted traffic jam and eventually reduce the drivers' on-road time, while the offline component solves how to generate speed profiles of a road network from historical trajectories. The challenging part of the routing problem of the online component lies in the computational complexity when determining if it is beneficial to wait on specific parking places and the time of waiting to maximize the benefit. To cope with this challenging problem, we propose two efficient algorithms using minimum on-road travel cost function to answer the query. We further introduce several approximation methods to speed up the query answering, with an error bound guaranteed. The offline speed profile generation component makes use of historical trajectories to provide the traveling time for the online component. Extensive experiments show that our method is more efficient and accurate than baseline approaches extended from the existing path planning algorithms, and our speed profile is accurate and space efficient.

Go slow to go fast: minimal on-road time route scheduling with parking facilities using historical trajectory

Shortest path query is a fundamental operation in various location-based services (LBS) and most of them process queries on the server-side. As the business expands, scalability becomes a severe issue. Instead of simply deploying more servers to cope with the quickly increasing query number, batch shortest path algorithms have been proposed recently to answer a set of queries together using shareable computation. Besides, they can also work in a highly dynamic environment as no index is needed. However, the existing batch algorithms either assume the batch queries are finely decomposed or just process them without differentiation, resulting in poor query efficiency. In this paper, we aim to improve the performance of batch shortest path algorithms by revisiting the problem of query clustering. Specifically, we first propose three query decomposition methods to cluster queries: Zigzag that considers the 1-N shared computation; Search-Space Estimation that further incorporates search space estimation; and Co-Clustering that considers the source and target’s spatial locality. After that, we propose two batch algorithms that take advantage of the previously decomposed query sets for efficient query answering: Local Cache that improves the existing Global Cache with higher cache hit ratio, and R2R that finds a set of approximate shortest paths from one region to another with bounded error. Experiments on a large real-world query sets verify the effectiveness and efficiency of our decomposition methods compared with the state-of-the-art batch algorithms.

Fast Query Decomposition for Batch Shortest Path Processing in Road Networks

On time-dependent graphs, fastest path query is an important problem and has been well studied. It focuses on minimizing the total travel time (waiting time + on-road time) but does not allow waiting on any intermediate vertex if the FIFO property is applied. However, in practice, waiting on a vertex can reduce the time spent on the road (for example, resuming traveling after a traffic jam). In this paper, we study how to find a path with the minimal on-road time on time-dependent graphs by allowing waiting on some predefined parking vertices. The existing works are based on the following fact: the arrival time of a vertex v is determined by the arrival time of its in-neighbor u, which does not hold in our scenario since we also consider the waiting time on u if u allows waiting. Thus, determining the waiting time on each parking vertex to achieve the minimal on-road time becomes a big challenge, which further breaks FIFO property. To cope with this challenging problem, we propose two efficient algorithms using minimum on-road travel cost function to answer the query. The evaluations on multiple real-world time-dependent graphs show that the proposed algorithms are more accurate and efficient than the extensions of existing algorithms. In addition, the results further indicate, if the parking facilities are enabled in the route scheduling algorithms, the on-road time will reduce significantly compared to the fastest path algorithms.

/pdf/minimal-on-road-time-route-scheduling-on-time-dependent-1ke80ruk24.pdf

Minimal on-road time route scheduling on time-dependent graphs

Route scheduling on time-dependent road network is slow due to its problem complexity of Ω(T(|V|log |V|+|E|)), where T is the size of the result's time-dependent function, |V| is the number of vertices and |E| is the number of edges. To make things worse, T grows larger as the route becomes longer or the query time interval becomes bigger, especially for a fastest path profile query whose time interval is 24 hours. In this paper, we aim to answer the fastest path profile query on time-dependent road network faster by extending the 2-hop labeling approach, which is fast in answering shortest distance query on the static graph. However, building an index on a time-dependent graph is both time and space consuming, so currently only online-search approach exist. Apparently, its query answering power is limited by the online searching. To solve this problem, we first propose the time-dependent hop on large road network by partitioning it into smaller sub-graphs. The index is built within and between the partitions, and is retrieved from disk during query answering with the help of sampling. Moreover, we propose an online approximation technique AT-Dijkstra and a bottom-up compression method to further reduce the label size, save construction time and speedup query answering. Experiments on real world road network show that our approach outperforms the state-of-art fastest path index approaches and can speed up the query answering by hundreds of times.

Time-Dependent Hop Labeling on Road Network

Location Based Social Networks (LBSN) promotes communications among subscribers. Utilizing online check-in data supplied via LBSN, Point-Of-Interest (POI) recommendation systems propose unvisited relevant venues to the users. Various techniques have been designed for POI recommendation systems. However, diverse temporal information has not been studied adequately. From temporal perspective, as visited locations during weekday and weekend are marginally different, we choose weekly intervals to improve effectiveness of POI recommenders. However, our method is also applicable to other similar periodic intervals. People usually visit tourist and leisure spots during weekends and work related places during weekdays. Similarly, some users perform check-ins mostly during weekend, while others prefer weekday predominantly. In this paper, we define a new problem to perform recommendation, based on temporal weekly alignments of users and POIs. We argue that locations with higher popularity should be more influential. Therefore, In order to solve the problem, we develop a probabilistic model which initially detects a user’s temporal orientation based on visibility weights of POIs visited by her. As a step further, we develop a recommender framework that proposes proper POIs to the user according to her temporal weekly preference. Moreover, we take succeeding POI pairs visited by the same user into consideration to develop a more efficient temporal model to handle geographical information. Extensive experimental results on two large-scale LBSN datasets verify that our method outperforms current state-of-the-art recommendation techniques.

Lei Li

Papers

Go slow to go fast: minimal on-road time route scheduling with parking facilities using historical trajectory

Fast Query Decomposition for Batch Shortest Path Processing in Road Networks

Minimal on-road time route scheduling on time-dependent graphs

Time-Dependent Hop Labeling on Road Network

Point-Of-Interest Recommendation Using Temporal Orientations of Users and Locations